Related papers: Branched Polymers
We discuss the extension of the empirical equation: $\left\langle s_{N}^{2}\right\rangle_{0}\propto g\,l^{2}$, where the subscript 0 denotes the ideal value with no excluded volume and $g$ the generation number from the root to the youngest…
On the basis of the thermodynamic theory of the excluded volume effects, we show that the size exponent varies abruptly, depending on the change of the segment concentration. For linear polymers, the exponent changes discontinuously from…
We point out some misconceptions in a recent paper by H. Aoki et al. [hep-th/9909060]. In particular, the claim that the two-point function of branched polymers behaves as 1/p^4 instead of 1/p^2 for large p is mistaken and in no way a…
The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a…
In [math-ph/0107005] we have proven that the generating function for self-avoiding branched polymers in D+2 continuum dimensions is proportional to the pressure of the hard-core continuum gas at negative activity in D dimensions. This…
We show that the spectral dimension on non-generic branched polymers with positive susceptibility exponent is given by $d_s=2/(1+\gamma)$. For those models with $\gamma<0$ we find that $d_s=2$.
Melonic graphs constitute the family of graphs arising at leading order in the 1/N expansion of tensor models. They were shown to lead to a continuum phase, reminiscent of branched polymers. We show here that they are in fact precisely…
The behavior of annealed branched polymers near adsorbing surfaces plays a fundamental role in many biological and industrial processes. Most importantly single stranded RNA in solution tends to fold up and self-bind to form a highly…
We investigate the excluded volume effects in good solvents for the isolated comb polymers having $\nu_{0}=1/4$. In particular, we investigate the change of the size exponent, $\nu$, defined by $\langle s_{N}^{2}\rangle\propto N^{2\nu}$,…
We establish an exact relation between self-avoiding branched polymers in D+2 continuum dimensions and the hard-core continuum gas at negative activity in D dimensions. We review conjectures and results on critical exponents for D+2 = 2,3,4…
We study the adsorption-desorption phase transition of directed branched polymer in $d+1$ dimensions in contact with a line by mapping it to a $d$ dimensional hard core lattice gas at negative activity. We solve the model exactly in 1+1…
Let $X_1,\ldots,X_N$, $N>n$, be independent random points in $\mathbb{R}^n$, distributed according to the so-called beta or beta-prime distribution, respectively. We establish threshold phenomena for the volume, intrinsic volumes, or more…
In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be…
Random walks and polygons are used to model polymers. In this paper we consider the extension of writhe, self-linking number and linking number to open chains. We then study the average writhe, self-linking and linking number of random…
We study simple branched coverings of degree d of the 2- and 3- dimensional sphere branched over oriented links. We demonstrate how to use braid charts to develop embeddings of these into $S^k \times D^2$ for $k=2,3 when $d=2,3$. This is an…
We show that the expected value of the mean width of a random polytope generated by $N$ random vectors ($n\leq N\leq e^{\sqrt n}$) uniformly distributed in an isotropic convex body in $\R^n$ is of the order $\sqrt{\log N} L_K$. This…
Let K be a d-dimensional convex body, and let $K^{(n)}$ be the intersection of n halfspaces containing $K$ whose bounding hyperplanes are independent and identically distributed. Under suitable distributional assumptions, we prove an…
It is proven that the volume of an infinitesimally flexible polyhedron in $R^3$ is a multiple root of its volume polynomial.
The shape of a polymer plays an important role in determining its interactions with other molecules and with the environment, and is in turn affected by both of them. As a consequence, in the literature the shape properties of a chain in…
The study of random surfaces, especially in the asymptotics of large genus, has been of increasing interest in recent years. Many geometrical questions have analogous formulations in the theory of random graphs with a large number of…